How to import morph targets into Blender?
One possible way is to import 1 mesh. Create a shape key as a base shape key. Import a second compatible mesh. Select the second mesh, and then shift+select the original base mesh, and on shape keys panel, click "Join as Shapes". Repeat to join all shape keys to 1 base mesh.

Try using THREE js to shift to one of the morph targets, then export multiple OBJ files and join them all in blender.